A rectangular parallelepiped is described near a cylinder with a base radius and a height of 5.

A rectangular parallelepiped is described near a cylinder with a base radius and a height of 5. find the volume of a parallelepiped

Since a rectangular parallelepiped is described around a cylinder, its bases are squares.

Let’s draw the radii OK and OH to the points of tangency of the edges of the parallelepiped. OK and OH are perpendicular to A1B1 and C1D1, then the side of the square at the base of the parallelepiped is 2 * OK = 2 * R = 2 * 5 = 10 cm.

Then Savsd = 10 * 10 = 100 cm2.

Let’s define the volume of the parallelepiped.

V = Savsd * AA1 = 100 * 5 = 500 cm3.

Answer: The volume of a parallelepiped is 500 cm3.